A385723 Numbers k such that m^m == m (mod k) where m = ceiling(k/2).
1, 2, 6, 7, 10, 14, 17, 18, 22, 23, 26, 30, 31, 34, 38, 41, 42, 46, 47, 50, 54, 58, 62, 66, 70, 71, 73, 74, 78, 79, 82, 86, 89, 90, 94, 97, 98, 102, 103, 106, 110, 113, 114, 118, 122, 126, 127, 130, 134, 137, 138, 142, 146, 150, 151, 154, 158, 162, 166, 167, 170
Offset: 1
Keywords
Programs
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Magma
[k: k in [1..200] | Modexp(m, m, k) eq m mod k where m is Ceiling(k/2)];
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Maple
q:= k-> (m-> 0=m&^m-m mod k)(ceil(k/2)): select(q, [$1..200])[]; # Alois P. Heinz, Jul 08 2025
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Mathematica
m[k_]:=Ceiling[k/2]; Select[Range[170], PowerMod[m[#], m[#], #]==Mod[m[#],#] &] (* Stefano Spezia, Jul 08 2025 *)
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PARI
isok(k) = my(m=ceil(k/2)); m == Mod(m, k)^m; \\ Michel Marcus, Jul 08 2025